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Math Help - Trigo Identities!

  1. #1
    gp3
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    Trigo Identities!

    hi guys,


    solve cos2x - 3cosx +2 = 0 for 0 < x < 360

    which formula should I use? is it the sum to product? I dont really know how to go about doing it! some advice pls!


    thanks!
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  2. #2
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    Grandad's Avatar
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    Hello gp3
    Quote Originally Posted by gp3 View Post
    hi guys,


    solve cos2x - 3cosx +2 = 0 for 0 < x < 360

    which formula should I use? is it the sum to product? I dont really know how to go about doing it! some advice pls!


    thanks!
    Use the identity:
    \cos 2x = 2\cos^2x-1
    Then simplify the LHS to get a quadratic in \cos x, which you can then factorise.

    Can you do it now?

    Grandad
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  3. #3
    gp3
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    so what I've got now is:

    2cos square x - 1 + 2 = 0
    2cos square x + 1 = 0
    (cosx+1)(cosx+1) = 0

    is this correct?
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by gp3 View Post
    so what I've got now is:

    2cos square x - 1 + 2 = 0
    2cos square x + 1 = 0
    (cosx+1)(cosx+1) = 0

    is this correct?
    No, you've missed out your 3cos(x) term.
    FYI 2cos^2(x)+1=0 has no real solutions. This is because x^2 \geq 0 for all real x. Adding 1 will always result in a positive answer where x is real



    The original question is \cos(2x) - 3\cos(x) +2 = 0

    What Grandad said is to change \cos(2x) to 2\cos^2(x)-1 - the 3cos(x) term is unaffacted.

    I have used square brackets to show this more effectively

    [2\cos^2(x) - 1] - 3cos(x) + 2 = 0

    You can simplify the constant terms to get it into the form ax^2+bx+c=0:

    2\cos^2(x) - 3cos(x) + 1 = 0

    You can the solve the quadratic using your favourite method although this one factorises.

    (2\cos (x) -1)(\cos (x) - 1) = 0
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  5. #5
    gp3
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    oh yea, thanks alot, I missed out 3cosx, guess I was too in a hurry.

    and btw, just a quick one, how do you factorise the eqn, from 2cos square x -3 cosx+1+0 to (2 cosx-1)(cosx-1)= 0 ?
    Last edited by gp3; February 19th 2010 at 01:59 AM.
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  6. #6
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    Quote Originally Posted by gp3 View Post
    oh yea, thanks alot, I missed out 3cosx, guess I was too in a hurry.

    and btw, just a quick one, how do you factorise the eqn, from 2cos square x -3 cosx+1+0 to (2 cosx-1)(cosx-1)= 0 ?
    Just solve it like any other quadratic equation. Treat cosx as x.
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